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Thoughts about an open rule set for wargaming. Are you good at math?http://www.warseer.com/forums/showthread.php?422756-Thoughts-about-an-open-rule-set-for-wargaming-Are-you-good-at-math&goto=newpost
Tue, 12 Sep 2017 19:27:01 GMTHello together,
my motivation:
After 17 years of wargaming in different systems I came to the conclusion that none fits truely my demands. So why not make up rules by my own. Sounds simple but many other had the same idea and failed (somehow). So there are some questions i asked myself before...

Hello together,

my motivation:
After 17 years of wargaming in different systems I came to the conclusion that none fits truely my demands. So why not make up rules by my own. Sounds simple but many other had the same idea and failed (somehow). So there are some questions i asked myself before starting to get into the rule stuff:

1. What makes a good set of rules for wargaming?

2. Why do so many self written rules fail?

And i answered these questions the following: 1.1. The game must be balanced. 1.2. You need to be able to make different decissions that have an impact on your and the enemy strategy. (Imagine a game where you can only shoot. Sounds quite boring). -> Add more depth than just moving/shooting/melee1.3. Minimize Random effects (Luck) that impact the game in a massive way. (Imagne you have a One-Shot-Mega-weapon that works only on a 6+. But when it works, you win the game. So in 5 out of 6 games you loose because you spent a hell of points for this weapon and in 1 of 6 games you win without doing anything) 1.4. The rules must be logical and somehow realistic. As realistic it can be when a flying Alien attacks a gigantic tank. :rolleyes:

2.1. The project started with a lot of motivation and when it becomes difficult the motivation disappears. -> Difficult questions first. Details later.2.2. The creator of the rules likes a special kind of army (mass/elite/flyers/...) or playstyle (melee/shooting/...). Therefore the rules are not balanced2.3. No one likes to learn a ton of new rules. -> Keep it simple

So lets start with the most difficult part. Balanced units.
To do so we have to make some assumtions. We have units with different stat lines that are able to deal damadge to the enemy units. At the moment I dont take into account whether these units are shooting or in melee. The just deal damadge to each other. I came up with the following preliminary stats (3 defensive stats / 3 offensive stats / Healthpoints):
Visibilty: Defines how easy/hard it is for the enemy to hit you
Armour: Selfexplaining
Toughness: Selfexplaining

Balistic/Melee Skill: Defines how easy/hard it is for your unit to hit the enemy
Penetration: Selfexplaining
Strength: Selfexplaining

Now comes the realy tricky part. How do you compare these values and define by a dice roll whether you hit/penetrate/wound your enemy?
How does it work the old GW style. You compre the values and if they are the same, you pass the test on a 4+. If your value is one higher than the enemy value you pass on a 3+. So that means if your value increases by 1 your probability to suceed the test increases by (3 out of 6 = 50%) (4 out of 6 = 66%) 16%. Correct? I dont think so. If you take 50% as your starting point your probability increased by 33% (the additional 1 out of the base 3). This is very important to understand my following thoughts.
Now if your value is two higher than the enemy value you will pass the test on a 2+. If you take 50% as starting point that increased your probability by 66% (the additional 2 out of the base 3). But if you take the +1 value from the previous example as sarting point your probablity increased by 25% (the additional 1 out of the base 4).

So if I increase one of the stat values by 1 I have to increase the point value of this unit. But how much? 33% (1st example) Or 25% (3rd Example). This effect gets even bigger with more difficult tests. If you pass your test on a 6+ (1 out of 6) and you improve it by 1 your probability doubled (2 out of 6). If you improve by another 1 your probability increased only by 50% (3 out of 6).

How to get rid of this? Quite easy: The amount the probability increases has to be constant if the stat values increase.
Example: You increase your Stat value by 1 -> your probability increases by 50% (base*1,5)
You increase your stat value by 2 -> your probability increases by ... 125% ((base*1,5)*1,5) or (base* 1,5^2)
you increase by 3 -> Probability increases by 237,5% (base*1,5^3)

Sounds good. In theory. How is it possible to increase the probability of a dice roll in a constant way? Lets make an easy example and increase it by 100%.
That means the first result is 1. The second result is 2, the third 4 and the fourth is 8.
So I need one side of the dice with a 1.
Another side with a 2
two additional sides with a 3
four additional sides with a 4
In this example I would need an 8 sided dice.

An increasement of 100% was too much in my opinion. So I tried something less. Maybe 50%
That means the first result is 1. The second is 1,5; the third is 2,25; the fourth is 3,375. Unfortunately a dice has only complete sides. But you can multiply all values to get a whole number. For example by 8
So i come to 8; 12; 18; 27
eight sides of the dice have a 1
four sides have a 2
six sides have a 3
nine sides have a 4
In this example i would need a dice with 27 sides. :/

After very much trying and a lot of excel files with macros I came to the following solution:
The increasement is 26,4%
And I do not start with a whole number but with 3,1 and round to the next whole number.
This leads to the following numbers:
3,1 ; 3,92 ; 4,95 ; 6,26 ; 7,91 ; 10,00 ; 12,64 ; 15,98 ; 20,20
3 ; 4 ; 5 ; 6 ; 8 ; 10 ;13 ; 16 ; 20
That means three sides with a 1
one side with a 2
one side with a 3
one side with a 4
two sides with a 5
two sides with a 6
three sides with a 7
three sides with a 8
four sides with a 9
In total a 20 sided dice.

So what I have now is a possibility to calculate a point value for a stat. For example a unit with strength 2 costs me 1,264^2 = 1,6 points. And a unit with strength 5 costs me 1,264^5 = 3,2 points. To pass the test i have to roll under or equal to the strength value. So i get two units with strength 2 or one unit with strength 5. The probability of the two units is two times 4 (three sides with 1 and one side with 2). The probability of the single unit is also 8 (three sides with 1, one side with 2, one side with 3, one side with 4 and two sides with 5).

--- tomorrow will follow more ---

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